RD Sharma Solutions Class 8 Practical Geometry Exercise 18.4

RD Sharma Class 8 Solutions Chapter 18 Ex 18.4 PDF Free Download

RD Sharma Solutions Class 8 Chapter 18 Exercise 18.4

Exercise 18.4

 

1. Construct a quadrilateral ABCD, in which AB = 6 cm, BC = 4 cm, CD = 4 cm, \(\angle B=95°\;\) and \(\angle C=90°\;\).

 

 

Steps of construction:

 

Step I: Draw BC = 4 cm.

Step II: Construct \(\angle ABC=95°\;\) at B.

Step III: With B as the center and radius 6 cm, cut off BA = 6 cm.

Step IV: Construct \(\angle BCD=90°\;\) at C.

Step V: With C as the center and radius 4 cm, cut off BA = 4 cm.

Step VI: Join CD.

The quadrilateral so obtained is the required quadrilateral.

 

2. Construct a quadrilateral ABCD, where AB = 4.2 cm, BC = 3.6 cm, CD = 4.8 cm, \(\angle B=30°\;\) and \(\angle C=150°\;\).

 

 

Steps of construction:

 

Step I: Draw BC = 3.6 cm.

Step II: Construct \(\angle ABC=30°\;\) at B.

Step III: With B as the center and radius 4.2 cm, cut off BA = 4.2 cm.

Step IV: Construct \(\angle BCD=150°\;\) at C.

Step V: With C as the center and radius 4.8 cm, cut off CD = 4.8 cm.

Step VI: Join AD.

The quadrilateral so obtained is the required quadrilateral.

 

3. Construct a quadrilateral PQRS, in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, \(\angle Q=75°\;\) and \(\angle R=120°\;\).

 

 

Steps of construction:

 

Step I: Draw QR = 2.5 cm.

Step II: Construct \(\angle PQr=75°\;\) at Q.

Step III: With Q as the center and radius 3.5 cm, cut off QP = 3.5 cm.

Step IV: Construct \(\angle QRS=120°\;\) at R.

Step V: With R as the center and radius 4.1 cm, cut off RS = 4.1 cm.

Step VI: Join PS.

The quadrilateral so obtained is the required quadrilateral.

 

4. Construct a quadrilateral ABCD given BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm and \(\angle D=100°\;\) and \(\angle C=95°\;\).

 

 

Steps of construction:

 

Step I: Draw DC = 4.4 cm.

Step II: Construct \(\angle ADC=100°\;\) at D.

Step III: With D as the center and radius 5.6 cm, cut off DA = 5.6 cm.

Step IV: Construct \(\angle BCD=95°\;\) at C.

Step V: With C as the center and radius 6.6 cm, cut off CB = 6.6 cm.

Step VI: Join AB.

The quadrilateral so obtained is the required quadrilateral.

 

5. Construct a quadrilateral ABCD, in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, \(\angle A=125°\;\) and \(\angle B=120°\;\).

 

 

Steps of construction:

 

Step I: Draw AB = 4.4 cm.

Step II: Construct \(\angle BAD=125°\;\) at A.

Step III: With A as the centre and radius 3.5 cm, cut off AD = 3.5 cm.

Step IV: Construct \(\angle ABC=125°\;\) at B.

Step V: With B as the centre and radius 4.7 cm, cut off BC = 4.7 cm.

Step VI: Join CD.

The quadrilateral so obtained is the required quadrilateral.

 

6. Construct a quadrilateral PQRS, in which \(\angle Q=45°\;\), \(\angle R=70°\;\), QR = 5 cm, PQ = 9 cm and RS = 7 cm.

 

 

Steps of construction:

 

Step I: Draw QR = 5 cm.

Step II: Construct \(\angle PQR=45°\;\) at Q.

Step III: With Q as the center and radius 9 cm, cut off QP = 9 cm.

Step IV: Construct \(\angle QRS=90°\;\) at R.

Step V: With R as the center and radius 7 cm, cut off RS = 7 cm.

Since, the line segment PQ and RS intersect each other, the quadrilateral cannot be constructed.

 

7. Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = 5 cm, \(\angle A=90°\;\) and \(\angle B=105°\;\).

 

 

Steps of construction:

 

Step I: Draw AB = 3 cm.

Step II: Construct \(\angle DAB=90°\;\) at A.

Step III: With A as the center and radius 5 cm, cut off AD = 5 cm.

Step IV: Construct \(\angle ABC=105°\;\) at B.

Step V: With B as the center and radius 3 cm, cut off BC = 3 cm.

Step VI: Join CD.

The quadrilateral so obtained is the required quadrilateral.

 

8. Construct a quadrilateral BDEF, where DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, \(\angle F=50°\;\) and \(\angle E=100°\;\).

 

 

Steps of construction:

 

Step I: Draw EF = 3.5 cm.

Step II: Construct \(\angle DEF=100°\;\) at E.

Step III: With E as the center and radius 4.5 cm, cut off DE = 4.5 cm.

Step IV: Construct \(\angle EFB=50°\;\) at F.

Step V: With F as the center and radius 6.5 cm, cut off FB = 6.5 cm.

Step VI: Join BD.

The quadrilateral so obtained is the required quadrilateral.

 

 

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